We present a quantum linear response (qLR) approach within an active-space framework for computing indirect nuclear spin-spin coupling constants, a key ingredient in NMR spectra predictions. The method employs the unitary coupled cluster (UCC) ansatz and its orbital-optimized variant (ooUCC), both suitable for quantum computing implementations, to evaluate spin-spin coupling constants via qLR. Test calculations on five small molecules are compared with CASCI, CASSCF, and conventional CCSD results. qLR with UCC/ooUCC yields spin-spin coupling constants comparable to classical methods. We further examine the role of orbital optimization and find that ooUCC markedly affects the computed couplings; orbital-optimized results show better agreement with CCSD. These findings indicate that orbital optimization is important for accurate NMR coupling predictions within quantum-computing-friendly correlated methods.
We present a quantum linear response (qLR) approach within an active-space framework for computing indirect nuclear spin-spin coupling constants, a key ingredient in NMR spectra predictions. The method employs the unitary coupled cluster (UCC) ansatz and its orbital-optimized variant (ooUCC), both suitable for quantum computing implementations, to evaluate spin-spin coupling constants via qLR. Test calculations on five small molecules are compared with CASCI, CASSCF, and conventional CCSD results. qLR with UCC/ooUCC yields spin-spin coupling constants comparable to classical methods. We further examine the role of orbital optimization and find that ooUCC markedly affects the computed couplings; orbital-optimized results show better agreement with CCSD. These findings indicate that orbital optimization is important for accurate NMR coupling predictions within quantum-computing-friendly correlated methods.
We present calculations of nuclear shielding constants, a key ingredient in nuclear magnetic resonance spectroscopy, within a quantum-computing-suitable framework. We employ quantum linear response (qLR) theory in combination with the unitary coupled cluster (UCC) ansatz and its orbital-optimized (oo-UCC), factorized (fUCC), and orbital-optimized factorized (oo-fUCC) variants. The methods are assessed for seven small molecules against CASCI, CASSCF, CCSD, and CCSD(T) reference calculations. The different UCC-based qLR approaches yield shielding constants in good agreement with comparable classical methods. Factorization, which is necessary for quantum-computing implementations, has only a negligible effect on the calculated shielding constants. Orbital optimization, in contrast, leads to substantial improvements, with oo-UCC and oo-fUCC showing markedly better agreement with CCSD and CCSD(T). Our results establish oo-fUCC combined with qLR as a promising approach for computing nuclear shielding constants on quantum computers.
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, particularly for systems that exhibit strong electronic correlation and for implementation on quantum computers. However, its practical application is limited to small chemical systems with small basis sets due to its steep computational scaling, which results from its nonterminating Baker-Campbell-Hausdorff expansion. Here, we introduce an active space UCCSD(4)/MP2 approach that leverages a fourth-order many-body perturbation theory truncation of UCCSD within a selected active space while treating external excitations at the MP2 level. We explore two variants: a composite method that sums separate internal and external contributions and an interacting method that couples the amplitudes for potentially greater accuracy. We test our approach on a range of systems, including molecules from the GW100 data set in their equilibrium geometries, a moderately correlated metaphosphate hydrolysis reaction, and the strongly correlated torsion of ethylene. Our results suggest that the interacting method with canonical orbitals is robust and stable for both weakly and moderately correlated systems and accurately reproduces the full UCCSD(4) potential energy curves, including only 15-25% of the virtual orbitals in its active space. In comparison, the composite formulation exhibits greater sensitivity to the choice of orbital basis and active space size, leading to less systematic behavior across the benchmark set. For ethylene torsion, a system dominated by strong static correlation, both the composite and interacting formulations employing canonical orbitals closely track the full UCCSD(4) reference while preserving the qualitative behavior of the parent method, including the breakdown in strongly multireference regimes. This active space framework offers a computationally tractable approach for modeling correlated molecules and reactions on classical computers and provides a viable path for scaling UCC calculations for resource-constrained quantum hardware.
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi–Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep scaling of its non-terminating Baker-Campbell-Hausdorff expansion. We introduce an active space UCCSD(4)/MP2 approach that leverages a fourth-order many-body perturbation theory truncation of UCCSD within a selected active space, while treating external excitations at the MP2 level. We explore two variants: a composite method that sums separate internal and external contributions and an interacting method that couples the amplitudes for greater accuracy. We test our approach on the GW100 dataset, a metaphosphate hydrolysis reaction, and the strongly correlated torsion of ethylene. Our results suggest that the interacting method with canonical orbitals is robust for weakly and moderately correlated systems and accurately reproduces the full UCCSD(4) potential energy curves using only 15-25% of the virtual orbitals in its active space. In comparison, the composite formulation exhibits greater sensitivity to the orbital basis and active space size, leading to less systematic behavior across the benchmark set. For ethylene torsion, a system dominated by strong static correlation, both composite and interacting formulations employing canonical orbitals closely track the full UCCSD(4) reference but do not alleviate the unphysical features inherited from the underlying single-reference UCCSD(4) description. This active space framework offers a tractable approach for modeling correlated molecules and reactions on classical computers and provides a viable path for scaling UCC calculations for resource-constrained quantum hardware.
Orbital optimization within the variational quantum eigensolver (VQE) framework is useful for improving active-space quality and accurately capturing electron correlation with shallow quantum circuits. The orbital-optimized unitary coupled cluster (OO-UCC) method [W. Mizukami et al., Phys. Rev. Res. 2, 033421 (2020)], in its original formulation, employs the orbital gradient and Hessian in a Newton--Laphson procedure. In this study, we propose sequential orbital-optimized unitary coupled cluster doubles (SOO-UCCD), extending the gradient-free sequential minimal optimization approach [K. M. Nakanishi et al., Phys. Rev. Res. 2, 043158 (2020)] to orbital rotation parameters. Based on the frequency structure implied by the algebraic properties of the orbital rotation generators, our method determines each orbital rotation angle from a nine-point energy profile. The energy landscape is evaluated by classically transforming the Hamiltonian integrals and contracting them with the reduced density matrices already measured for the VQE energy evaluation. This allows for orbital optimization without evaluating the orbital gradient or Hessian. By building on the core benefits of the OO-UCC framework, our method provides a gradient-free and hyperparameter-free orbital-optimization procedure. State-vector simulations for LiH in the STO-3G basis show that SOO-UCCD reproduces UCCSD-level accuracy along the bond-stretching curve and exhibits macro-iteration convergence comparable to that of L-BFGS-based orbital optimization.
We introduce a unitary coupled-cluster (UCC) ansatz termed k -UpCCGSD that is based on a family of sparse generalized doubles operators, which provides an affordable and systematically improvable unitary coupled-cluster wave function suitable for implementation on a near-term quantum computer. k -UpCCGSD employs k products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized single and double excitation operators (UCCGSD), as well as with the standard ansatz employing only single and double excitations (UCCSD). k -UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of, compared with for UCCGSD, and for UCCSD, where N is the number of spin orbitals and η is the number of electrons. We analyzed the accuracy of these three ansätze by making classical benchmark calculations on the ground state and the first excited state of H 4 (STO-3G, 6-31G), H 2 O (STO-3G), and N 2 (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that k -UpCCGSD offers a good trade-off between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. UCCGSD is also found to be more accurate than UCCSD but at a greater cost for implementation. Excited states are calculated with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. We demonstrate that using a specialized multideterminantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved.